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Large geographic areas should host a greater diversity of crime compared with small geographic areas. This proposition is reasonable given that larger geographic areas should not only support more crime but also contain a greater diversity of criminogenic settings. This article uses a neutral model to characterize crime richness as a function of area. The model starts with two neutral assumptions: 1) that all environments are statistically equivalent and exert no influence on what types of crimes occur there; and 2) that different crime types occur independently of one another. The model produces rigorous predictions for the mean and variance in crime richness with increasing area. Tests of the model against a sample of 172,055 crimes occurring in Los Angeles during the year 2013 are qualitatively consistent with neutral expectations. The model is made quantitatively consistent by constant scaling. Resampling experiments show that at most 20 percent of the mean crime richness is attributable to nonrandom clustering and assortment of crime types. A modified neutral model allowing for variation crime concentration is consistent with observed variance in crime richness. The results suggest that very general and largely neutral laws may be driving crime diversity in space. [ABSTRACT FROM AUTHOR]

Within any type of system, the actors in the system inevitably compete over resources. With competition comes the possibility of conflict. To minimize such effects, actors often will partition the system into geographic territories. It is against the larger ecological backdrop of competition and conflict that we examine territory formation among urban street gangs. Although previous studies have examined the social and built environment where gangs form, and how the presence of a gang influences local levels of violence, we know little about how competitive interactions are tied to the formation and maintenance of gang territories. We use formal spatial Lotka-Volterra competition models to derive hypotheses about competition-driven territory formation. By using data on 563 between-gang shootings, involving 13 rival street gangs in the Hollenbeck Policing Division of Los Angeles, we show that violence strongly clusters along the boundaries between gangs in a way that is quantitatively predicted by the theory. The results suggest that even weak competitive interactions between gangs are sufficient to drive gang territory formation without recourse to other processes or assumptions. [ABSTRACT FROM AUTHOR]

The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing. [ABSTRACT FROM AUTHOR]